A lot of this comes from regional variations in language. In the deep south, barbecue is smoked meat, served with a selection of sauces. It's cooked on a smoker. Nobody here, except for northern transplants, refer to *a* barbecue. If you're referring to a the thing you use to cook outside with charcoal or gas, that's a grill (and even what Weber calls it). If you're referring to an outdoor even when grilled meats are served, that is a cookout.